The Network as a Storage Device: Dynamic Routing with Bounded Buffers

Abstract

We study dynamic routing in store-and-forward packet networks where each network link has bounded buffer capacity for receiving incoming packets and is capable of transmitting a fixed number of packets per unit of time. At any moment in time, packets are injected at various network nodes with each packet specifying its destination node. The goal is to maximize the throughput, defined as the number of packets delivered to their destinations.In this paper, we make some progress on throughput maximization in various network topologies. Let n and m denote the number of nodes and links in the network, respectively. For line networks, we show that Nearest-to-Go (NTG), a natural distributed greedy algorithm, isÕ( √ n)-competitive, essentially matching a known ( √ n) lower bound on the performance of any greedy algorithm. We also show that if we allow the online routing algorithm to make centralized decisions, there is a randomized polylog(n)-competitive algorithm for line networks as well as for rooted tree An extended abstract appeared in the 72 Algorithmica (2009) 55: 71-94 networks, where each packet is destined for the root of the tree. For grid graphs, we show that NTG has a competitive ratio of˜ (n 2/3 ) while no greedy algorithm can achieve a ratio better than ( √ n). Finally, for arbitrary network topologies, we show that NTG is˜ (m)-competitive, improving upon an earlier bound of O(mn).

Packet Forwarding Algorithms in a Line Network

“…The objective is to maximize a function of the transmitted packets, for instance their number, size, or (weighted) value. Work in this model has mostly employed competitive analysis, see [14][15][16][17][18][19][20][21][22][23][24][25]. The problem has also been studied when the routers have shared but limited memory [26].…”

An O(logn)-Competitive Online Centralized Randomized Packet-Routing Algorithm for Lines

“…In [AKOR03], a lower bound of Ω( √ n) was proved for the greedy algorithm on directed lines if the buffer size B is at least two. For the case B = 1 (in a slightly different model), an Ω(n) lower bound for any deterministic algorithm was proved by [AZ05,AKK09]. Both [AZ05] and [AKK09] developed, among other things, online randomized centralized algorithms for directed paths with B > 1.…”

“…For the case B = 1 (in a slightly different model), an Ω(n) lower bound for any deterministic algorithm was proved by [AZ05,AKK09]. Both [AZ05] and [AKK09] developed, among other things, online randomized centralized algorithms for directed paths with B > 1. In [AKK09] an O(log 3 n)-competitive algorithm was presented if the buffer size B is at least 2.…”

“…Both [AZ05] and [AKK09] developed, among other things, online randomized centralized algorithms for directed paths with B > 1. In [AKK09] an O(log 3 n)-competitive algorithm was presented if the buffer size B is at least 2. For the case B = 1, they presented a randomizedÕ( √ n)-competitive distributed algorithm.…”

“…(II) Our algorithm works also for buffers of size B = 1. (III) We consider also the parameter c of the capacity of the links ( [AZ05,AKK09] considered only the case c = 1).…”